One-Dimensional Method
The inverse kinematic problem for six-DOF manipulators reduces to a five-DOF one when the first or the last joint variable is known. Equation (7.1) becomes
A2 A3 A4 A5 A6 =Q, (7.45)
with
Q = A1-1 P (7.46)
when G1 is known, and
A1 A2 A3 A4 A5 = Q, (7.47)
with
Q = P 61B5 (7.48)
if 06 is known. In both cases, a five-DOF problem is
obtained. When the resulting five-DOF problem is solvable in closed form, knowledge of 81 or E6 is then sufficient to yield a complete solution set. The inverse kinematic
problem then reduces to finding one joint angle which can be accomplished by a one-dimensional iterative technique. In chapter 6, we found that a sufficient condition for closed form solutions of 5-DOF manipulators is that they have one of the special structures listed at the end of Chapter 6. Six-DOF arms that include a five-DOF segment with this type of geometry can then be solved using a onedimensional iterative method. This iterative technique can be implemented in much the same way as described in Chapter
..